Brief paper: Identification for robust H2 deconvolution filtering

Authors:
Xavier Bombois;Håkan Hjalmarsson;Gérard Scorletti
Affiliations:
Delft Center for Systems and Control, Mekelweg 2, 2628 CD Delft, The Netherlands;ACCESS Linnaeus Center, Electrical Engineering, KTH-Royal Institute of Technology, S-100 44 Stockholm, Sweden;Laboratoire Ampère, Ecole Centrale de Lyon, 36 avenue Guy de Collongue - 69134 Ecully Cedex, France
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

This paper addresses robust deconvolution filtering when the system and noise dynamics are obtained by parametric system identification. Consistent with standard identification methods, the uncertainty in the estimated parameters is represented by an ellipsoidal uncertainty region. Three problems are considered: (1) computation of the worst case H"2 performance of a given deconvolution filter in this uncertainty set; (2) design of a filter which minimizes the worst case H"2 performance in this uncertainty set; (3) input design for the identification experiment, subject to a limited input power budget, such that the filter in (2) gives the smallest possible worst case H"2 performance. It is shown that there are convex relaxations of the optimization problems corresponding to (1) and (2) while the third problem can be treated via iterating between two convex optimization problems.